MeanLinear: Linear Mean Function
In duckmayr/gpmss: Gaussian Process Models for Social Science
Description
Details
Super class
Public fields
Methods
Description
A linear mean.
Details
This function gives a linear mean; denoting its hyper vector by
(α, β), where α is an (optional) intercept,
and β is a vector of coefficients whose length is the same
as the number of columns in X, then for an input matrix X,
the prior mean is α + X β.
Note: Usually in regression models we would instead use the notation
X β, where the first element of β is a coefficient
for the intercept and X has a column of ones prepended to it.
The reason we do not do this in GP regression and classification is
because adding a one column to the design matrix is generally not
desirable in terms of the inputs to the kernel, and is not generally
helpful for other mean functions as well. So, we simply address the
intercept issue by adding a hyperparameter to a linear mean function
that is not involved with any multiplication with predictors.
Super class
gpmss::MeanFunction -> MeanLinear
Public fields
nameA character vector of length one giving the mean
function's name; "linear"
hypersA numeric vector giving the mean function's
hyperparameters
interceptA logical vector of length one; does the linear
mean include an intercept?
Methods
Public methods
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Inherited methods
Method mean()
Compute function prior mean
Usage
MeanLinear$mean(X, hypers = NULL)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the
mean function. If NULL (the default), the hypers data
member is used.
Method parameter_derivative()
Compute partial derivatives of mean function with respect to
its hyperparameters
Usage
MeanLinear$parameter_derivative(X, hypers = NULL, param = 1)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the
mean function. If NULL (the default), the hypers data
member is used.
paramAn integer vector of length one; which element of
hypers should the derivative be taken with respect to?
The default is 1
Method input_derivative()
Compute partial derivatives of mean function with respect to
its inputs
Usage
MeanLinear$input_derivative(X, hypers = NULL, dimension = 1)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the
mean function. If NULL (the default), the hypers data
member is used.
dimensionan integer vector of length one giving the dimension
of X with respect to which the derivative is being taken; the
default is 1
Method new()
Create a new MeanLinear object
Usage
MeanLinear$new(hypers = 0, intercept = TRUE)
Arguments
hypersA numeric vector giving hyperparameters for
the mean function. If the provided hypers are of length one,
it will be recycled as necessary to match the number of columns
of X when used.
interceptA logical vector of length one; should the linear
mean include an intercept? The default is TRUE.
Method clone()
The objects of this class are cloneable with this method.
Usage
MeanLinear$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
duckmayr/gpmss documentation built on Nov. 8, 2021, 5:48 a.m.
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Description Details Super class Public fields Methods
Description
A linear mean.
Details
This function gives a linear mean; denoting its hyper vector by (α, β), where α is an (optional) intercept, and β is a vector of coefficients whose length is the same as the number of columns in X, then for an input matrix X, the prior mean is α + X β.
Note: Usually in regression models we would instead use the notation X β, where the first element of β is a coefficient for the intercept and X has a column of ones prepended to it. The reason we do not do this in GP regression and classification is because adding a one column to the design matrix is generally not desirable in terms of the inputs to the kernel, and is not generally helpful for other mean functions as well. So, we simply address the intercept issue by adding a hyperparameter to a linear mean function that is not involved with any multiplication with predictors.
Super class
gpmss::MeanFunction -> MeanLinear
Public fields
nameA character vector of length one giving the mean function's name; "linear"
hypersA numeric vector giving the mean function's hyperparameters
interceptA logical vector of length one; does the linear mean include an intercept?
Methods
Public methods
Inherited methods
Method mean()
Compute function prior mean
Usage
MeanLinear$mean(X, hypers = NULL)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the mean function. If NULL (the default), the hypers data member is used.
Method parameter_derivative()
Compute partial derivatives of mean function with respect to its hyperparameters
Usage
MeanLinear$parameter_derivative(X, hypers = NULL, param = 1)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the mean function. If NULL (the default), the hypers data member is used.
paramAn integer vector of length one; which element of
hypersshould the derivative be taken with respect to? The default is 1
Method input_derivative()
Compute partial derivatives of mean function with respect to its inputs
Usage
MeanLinear$input_derivative(X, hypers = NULL, dimension = 1)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the mean function. If NULL (the default), the hypers data member is used.
dimensionan integer vector of length one giving the dimension of X with respect to which the derivative is being taken; the default is 1
Method new()
Create a new MeanLinear object
Usage
MeanLinear$new(hypers = 0, intercept = TRUE)
Arguments
hypersA numeric vector giving hyperparameters for the mean function. If the provided hypers are of length one, it will be recycled as necessary to match the number of columns of X when used.
interceptA logical vector of length one; should the linear mean include an intercept? The default is TRUE.
Method clone()
The objects of this class are cloneable with this method.
Usage
MeanLinear$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
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